As a warning: While C99 is a really nice language - especially over C89 - please note that the Visual Studio C compiler still does not support the full C99 specification, and it is not possible at all to compile C99 as C++ code (which sometimes is useful).
I usually recommend to write library-level code in the "subset of C99 which compiles both in C and C++ mode on GCC, clang and MSVC". This is basically a version of C that's somewhere C89 and C99 (basically a "C95").
Another quite valid option is to define a pure C-API first, but implement the "inner library code" in a simple C++ (just be careful with "modern C++", since this usually results in increased compilation time and binary size).
I usually recommend to write library-level code in the "subset of C99 which compiles both in C and C++ mode on GCC, clang and MSVC". This is basically a version of C that's somewhere C89 and C99 (basically a "C95").
Another quite valid option is to define a pure C-API first, but implement the "inner library code" in a simple C++ (just be careful with "modern C++", since this usually results in increased compilation time and binary size).